Third-Order Ambisonic Extensions for Max/MSP with Musical
Applications
Graham Wakefield
Graduate Program in Media Arts and Technology, University California Santa Barbara
wakefield@mat.ucsb.edu
• To develop tools for prototyping virtual
environments within multi-user facilities such as the
UCSB CNSI AlloSphere (Pope 2005,
http://www.mat.ucsb.edu/allosphere/).
Abstract
This paper describes a package of extensions (externals) for
Cycling ‘74’s Max/MSP software to facilitate the
exploration of Ambisonic techniques of up to third order.
Areas of exploration well suited to the Max/MSP
environment and techniques for composition within the
Ambisonic domain using the presented externals are
described.
1
Introduction
Ambisonics (Gerzon 1973) is a technique to re-create
the impression of (or synthesize) a spatial sound-field;
alternative techniques include Wave Field Synthesis
(Berkhout 1988) and Vector Base Panning (Pulkki 1997).
Ambisonics is a two-part process of encoding recorded or
virtual spatial sources into an Ambisonic domain
representation, and then decoding this representation onto
an array of spatial outputs (typically loudspeakers). The
Ambisonic domain is a multi-channel representation of
spatial sound fields based upon cylindrical (2-D) or
spherical (3-D) harmonics.
First-order Ambisonics, also known as the B-Format,
encode sound-fields as an omni-directional signal (named
W) plus three additional difference signals for each of the
axes X, Y and Z. Higher Order Ambisonics (HOA) uses
higher ordered spherical harmonics for additional encoded
signals, increasing the detail of directional information and
expanding the acceptable listening area of the decoded
spatial sound field (Malham 2003).
This paper describes a package of externals developed
by the author to add Ambisonic capabilities to Max/MSP up
to third order with full access to the Ambisonic domain
signals. Max/MSP (Puckette 1988, Zicarelli 1998) is a
flexible visual data-flow programming environment with
audio signal processing capabilities, including a C API for
developers to extend the functionality of Max/MSP by
building extensions (externals).
The rationale behind the development of the presented
externals is twofold:
•
To facilitate rapid experimentation and prototyping
of Ambisonic-domain processing techniques (some
examples follow in this paper)
123
Ambisonic extensions for Max/MSP have until recently
been limited to first-order representations (e.g. Courribet
and Béguin 2005). Concurrently with the present set of
externals, The Institute for Computer Music and Sound
Technology ICST of the Zurich School of Music, Drama
and Dance (Hochschule Musik und Theater Zürich HMT)
announced a set of Ambisonics externals for Max/MSP, and
both sets of externals share many capabilities. Beneficially,
both the ICST externals and those described in this paper
can be used together within the same application.
2
About the Ambisonic externals
The package described in this paper contains several
different externals to encapsulate distinct elements of the
Ambisonic process. Some aspects of these externals,
however, are common to all. Instantiation arguments of the
externals set the order of encoding, and whether they are
two-dimensional (pantophonic) or three-dimensional
(periphonic) formats, determining how many signal inlets
and/or outlets the externals require. Ambisonic domain
inlets and outlets are labeled by the channel naming
conventions of Jérôme Daniel (2000) to assist the correct
connection of signal graphs.
2.1
Encoding sources
A monophonic virtual or microphone source is encoded
to the Ambisonic representation using the external
ambi.encode~. The monophonic source signal is connected
to the first inlet, and the azimuth and elevation control
signals (in degrees or radians) are connected to the second
and third inlets respectively (Figure 1). The outlets of the
external are the encoded Ambisonic representation.
By default, the azimuth and elevation signal inputs are
sampled at block-rate with linear interpolation, however a
more CPU intensive sample accurate mode (causing the
encoding matrix to be recalculated at every sample) is
available if required by particular applications (e.g. fast
moving sources).
equally spaced on the radius of a circle around the listener.
In the 3-D case, only five regular polyhedra exist (the
platonic solids), and thus usually a semi- or quasi-regular
layout is sought, and maintaining an equatorial ring is
usually preferred for psychoacoustic reasons. Hollerweger
(2006) provides extensive detail and MATLAB code for the
choice of speaker layouts in Ambisonic decoding.
Ambi.decode~ uses the projection method to generate
the decoding matrix, which is less sensitive to the regularity
of the speaker layout than the pseudo-inverse method.
Nevertheless, directional and energy balance distortions will
increase as the layout becomes more irregular (Daniel 2000,
Hollerweger 2006).
Figure 1. A simple Max/MSP patch, encoding a virtual
source (white noise) at centre-front into a 3-D, firstorder (B-Format) representation, rotated by π/2 radians,
and decoded onto an array of four loudspeakers.
Since one of the principal benefits of Ambisonics is the
compact representation of a complex sound field, the author
provided an external that can encode up to 16 individually
positioned virtual sources to a mixed encoded output, named
ambi.encoden~. The third instantiation argument defines
how many monophonic sources the object will encode, and
thus how many signal inlets it will have. Spatial
orientations of azimuth and elevation can be specified (in
degrees or radians) for individual sources using Max
messages (Figure 2); ambi.encoden~ is better suited to static
or infrequently moving objects since encoding matrices are
recalculated at message rate.
Ambi.granulate~ offers the ability to create even larger
numbers of spatial events, based upon the granulation of a
buffered delay line – creating thousands of discrete
Ambisonic events per second would be otherwise difficult
in Max/MSP. The encoding matrix of each grain is
calculated when the grain is scheduled. Parameters for
amplitude, azimuth, elevation, duration, inter-onset time,
delay etc. are set (as centre value and deviation range) using
Max messages, and the sizes of the delay buffer and
maximum grain concurrency per block are specified as
instantiation arguments (limited by available RAM).
2.3
Decoding the sound field
The Ambisonic domain signal representation is decoded
into a multi-channel array of channels, typically for a
loudspeaker array, using the ambi.decode~ external. The
number of output channels is determined by instantiation
arguments, and the relative orientations for each speaker are
specified using Max messages. If no speaker orientations
are specified, a clockwise horizontal ring beginning from
centre-left is assumed as by default (Figures 1,2).
It should be noted that Ambisonics works best with
regular orthonormal speaker layouts (Daniel 2000). For the
2-D case, a regular (polygonal) layout has all speakers
124
Figure 2. A Max/MSP patch encoding 16 individually
positionable and tunable band-passed noise sources to a
third-order Ambisonic representation, then decoded to a
16-speaker array.
Several different encoding conventions exist to scale
Ambisonic signals at various orders. The original B-Format
definition specified a scalar of √2 for the W channel, while
the Furse-Malham set (Malham 1999) scales second-order
signals to achieve normalized values in the Ambisonic
domain, and Daniel (2000) specified up to third order
without normalizing weights except for the original √2 W
channel. In the presented Max/MSP externals the author
opted to employ the same convention as presented by Daniel
(2000) since the floating point signal operations of
Max/MSP obviate the need for normalization, while
retaining compatibility with existing B-Format recordings.
The ambi.decode~ external includes sets of order
coefficients from the literature (basic, in-phase, max-rE),
which can be recalled using Max messages. In addition,
Max messages can be used to directly set the balance
between the zeroth- (omnidirectional), first-, second- and
third-order encoded channels, to enhance or suppress the
spatial separation, or to improve the spatial impression for
combinations of distinct order representations and/or
unusual speaker arrays.
2.3
Rotating the sound field
An Ambisonic sound-field can be rotated using a set of
matrix operations (Malham 2003). The ambi.rotate~
external can be inserted into the Ambisonic domain signal
stream and used to rotate an entire sound field (of up to third
order) around one or more of the principal axes (Figures
1,2). Max messages with float arguments of ‘rotate’, ‘tilt’
and ‘tumble’ will transform the field around the Z, Y and X
axes respectively. When tilt and tumble are set to zero (the
default), the rotation calculations are simplified for
efficiency.
Rotating an entire sound field can be much more
efficient than rotating each individual source when the
number of sources is greater than the number of encoding
channels. Sound field rotation is well suited to the
sonification of a virtual environment, where navigation will
shift apparent orientations of all sound sources in unison.
3
and the LFE channel submixed into the omnidirectional W
Ambisonic channel, and the Ambisonic signals could then
be decoded onto a larger array of loudspeakers.
3.2
Simulating distance cues
Spatial hearing based upon directional and distance
based cues. Ambisonics is a convenient approach to tackle
directional information since it is based on spherical
coordinates. Distance is not represented in the standard
Ambisonic encoding (for mathematical reasons all sources
are assumed to lie on the surface of a unit sphere), however
distance is a vital component in virtual environment
simulation. Distance cues can be used in combination with
Ambisonics however (Malham 1998), and existing
Max/MSP signal processing objects can be used alongside
the Ambisonics externals accordingly (Figure 3).
The Ambisonic externals in use
The Ambisonic externals described in this paper give the
designer of a signal graph a great deal of flexibility to define
spatial sound fields and explore spatial manipulation
techniques, due to the direct access they provide to
individual Ambisonic channels, and the comprehensive
range of signal and event processing tools that the
Max/MSP environment itself provides. In this section a
number of possible areas of exploration will be described.
A particular benefit of the Ambisonic encoding is that
summing the encoded channels will correctly superpose
spatial representations encoded at the same order. A
multitude of sources may therefore be individually
manipulated before mixing down to a single Ambisonic
representation to be decoded over many loudspeakers.
Mixing Ambisonic signals of different orders is also
possible, at the cost of spatial balance.
3.1
Using existing spatial recordings
A spatial sound field representation can be captured to
disk as a multi-channel sound file using standard Max/MSP
objects such as sfrecord~, record~, though it may be
necessary to apply normalization to the signals when
recording to an integer based file format. Similarly, an
Ambisonic sound file can be played back over a speaker
array using the Max/MSP built-in objects sfplay~, play~ etc.
connected to an ambi.decode~ object. Placing the sound
field manipulations between the file player objects and the
decoder allow the real-time transformation of the stored
Ambisonic sound field at playback.
Recordings for particular speaker arrangements can be
somewhat generalized to larger speaker arrays using
Ambisonics. For example, a typical 5.1 surround layout can
be simulated in Ambisonics by a set of 5 virtual sources
placed around the listener. A sound source encoded for 5.1
could be spatialized using ambi.encoden~ with five inputs,
Figure 3: Simulating distance cues in combination with
Ambisonics. Inset shows the reverb_by_distance subpatcher.
Distance cues might include processing a sound source
before encoding (including decreasing amplitude with
increasing distance, applying IIR filters to simulate air
absorption and near-field compensation (Daniel 2003), and
using variable delays to mimic Doppler shift), as well as
mixing in ‘room effect’ first reflection and tail
reverberations to the encoded sound field according to
distance and/or position.
The Jitter extensions to Max/MSP include bindings to
OpenGL for three-dimensional rendering. Ambisonic
encoding alongside distance cues can facilitate the
125
auralization of rendered virtual worlds within a single
application.
3.3
Processing in the Ambisonic domain
Access to a sample-accurate Ambisonic encoder
suggests experimentation with high-frequency variations in
spatial orientation. Furthermore, access to the Ambisonic
domain signals within a flexible DSP environment invites
experimentation with new manipulations of the sound field,
and the possibility of directly synthesizing the directional
difference signals (rather than or in addition to encoding
virtual sources). For example, a relatively simple FM
synthesis technique when used to generate differential
signals of the Ambisonic domain itself may result in quite
complex and new spatial sound events. Certainly it must be
valid to attempt the extension of existing synthesis
techniques with spatial parametrics, if possible! The author
has for example explored passing comb filters in a feedback
matrix across the Ambisonic channels, producing subtle,
complex and chaotic spatial images warranting further
investigation.
Certain signal processes are quite expensive and thus
often cannot be duplicated per channel for large speaker
arrays. Because the number of Ambisonic domain signals is
almost always less than the number of loudspeakers, it can
be more efficient to perform expensive operations in the
Ambisonic domain.
The author has employed a similar approach in order to
spatialize individual bands of a spectral resynthesis process.
The spectral resynthesis produces a summed monophonic
output from a large number of individual bands, but
provides independent amplitude control for each voice. To
spatialize the individual bands, four spectral resynthesizers
were Ambisonic encoded as four virtual speaker locations
(in a regular tetrahedral pyramid layout), and then decoded
onto an array of 16 real loudspeakers. The amplitude of a
particular frequency band can thus be modulated spatially
quite efficiently using four rather than sixteen banks, and
although there is a tradeoff of spatial accuracy, the sonic
effect is quite effective. A similar approach might be taken
to simulate frequency variant radiation patterns, as
described by Daniel (2003).
4
Conclusions
Ambisonics is a powerful and efficient means to work
with spatial digital audio. Second- and third-order
Ambisonics involve complex algorithms that are more
efficiently and conveniently managed using compiled C
externals than existing Max/MSP objects. The open-ended
nature of the Max/MSP signal graph architecture, and the
access to the Ambisonic domain signals that the presented
externals deliver, provide a flexible environment for
exploring new kinds of signal manipulations and techniques
for composition in the Ambisonic domain.
126
The extensions described in this paper constitute a
minimal set to begin exploring Ambisonics in electroacoustic composition, however a few key areas are currently
under consideration for future development. Speaker arrays
of 30 or more may demand the development of fourth, fifth
or higher order encoding and decoding externals to expand
the sweet area. A HRTF decoder for headphone listening
would be a welcome addition.
At the time of writing, the externals are available as
binaries
from
the
author’s
website
(http://www.grahamwakefield.net).
5
Acknowledgments
The presented Ambisonic extensions to Max/MSP were
inspired by work on the CSL signal-processing library
(Pope, Ramakrishnan, 2003) alongside Florian Hollerweger
(IEM, Graz, Austria), and Jorge Castellanos (MAT, Santa
Barbara, USA).
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